Find a unit vector in the direction of the resultant of the vectors ` hat i- hat j+3 hat k ,""2 hat i+ hat j-2 hat k" and " hat i +2 hat j-2 hat k""dot`

Explanation

To find a unit vector in the direction of the resultant of the given vectors, we will follow these steps:

### Step 1: Define the Vectors
Let the vectors be defined as follows:
- \( \mathbf{a} = \hat{i} - \hat{j} + 3\hat{k} \)
- \( \mathbf{b} = 2\hat{i} + \hat{j} - 2\hat{k} \)
- \( \mathbf{c} = \hat{i} + 2\hat{j} - 2\hat{k} \)

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